The easiest band to get into in the genre is Explosions in th Sky, in my opinion, check out their song "Your Hand In Mine". If anyone's ever seen the TV show Friday Night Lights (Soooooo good!) then you'll know this song as the theme tune, best song ever in my opinion. Should be on YouTube or something. Godspeed is alot more difficult to get into, almost all of their tracks top the 20 minute mark and there's alot of silence and static in their music, not the most accessible stuff you can find. Mogwai is quite easy to listen to, shorter tracks makes it easier to pick just one track to listen to rather than having to listen to the whole record to get the true feel of it.
YouTube - Crimson in the Sky - There you go, wait until around 40 seconds in and then turn your volume up. The video is nothing to do with the song, someone just put it together and it's the only full, studio version of the song I could find. Enjoy it, cherish it even because the first time you hear the song it's a big thing, or it was for me anyway.